DEFINITIONS.
I. By cause of itself I understand that, the essence of which involves existence: or that, the nature of which can only be considered as existent.
II. A thing finite is that which can be limited (terminari potest) by another thing of the same nature —ergo, body is said to be finite because it can always be conceived as larger. So thought is limited by other thoughts. But body does not limit thought, nor thought limit body.
III. By substance I understand that which is in itself, and is conceived per se– that is, the conception of which does not require the conception of anything else as antecedent to it.
IV. By attribute I understand that which the mind perceives as constituting the very essence of substance.
V. By modes I understand the accidents (affectiones) of substance; or that which is in something else, through which also it is conceived.
VI. By God I understand the being absolutely infinite; that is, the substance consisting of infinite attributes, each of which expresses an infinite and eternal essence.
Explication, I say absolutely infinite, but not in suo genere; for to whatever is infinite, but not in suo genere, we can deny infinite attributes; but that which is absolutely infinite, to its essence pertains everything which implies essence, and involves no negation.
VII. That thing is said to be free which exists by the sole necessity of its nature, and by itself alone is determined to action. But that is necessary, or rather constrained, which owes its existence to another, and acts according to certain and determinate causes.
VIII. By eternity I understand existence itself, in as far as it is conceived necessarily to follow from the sole definition of an eternal thing.
AXIOMS.
I. Everything which is, is in itself, or in some other thing.
II. That which cannot be conceived through another, per aliud must be conceived, per se.
III. From a given determinate cause the effect necessarily follows, and vice versa. If no determinate cause be given, no effect can follow.
IV. The knowledge of an effect depends on the knowledge of the cause, and includes it.
V. Things that have nothing in common with each other cannot be understood by means of each other – that is, the conception of one, does not involve the conception of the other.
VI. A true idea must agree with its original in nature.
VII. Whatever can be clearly conceived as non-existent does not, in its essence, involve existence.
PROPOSITIONS.
I. Substance is prior in nature to its accidents. Demonstration. Per definitions three and five.
II. Two substances, having different attributes, have nothing in common with each other. Dem. This follows from def. three; for each substance must be conceived in itself and through itself; in other words, the conception of one does not involve the conception of the other.
III. Of things which have nothing in common, one cannot be the cause of the other. Dem. If they have nothing in common, then (per axiom five) they cannot be conceived by means of each other; ergo (per axiom four,) one cannot be the cause of the other. – Q. E. D.
IV. Two or more distinct things are distinguished among themselves, either through the diversity of their attributes, or through that of their modes. Dem. Everything which is, in itself, or in some other thing (per ax. one) – that is (per def. three and five,) there is nothing out of ourselves (extra intellectum, outside the intellect) but substance and its modes. There is nothing out of ourselves whereby things can be distinguished amongst one another, except substances, or (which is the same thing, per def. lour) their attributes and modes.
V. It is impossible that there should be two or more substances of the same nature, or of the same attributes. Dem. If there are many different substances they must be distinguished by the diversity of their attributes or of their modes (per prop. 4.) If only by the diversity of their attributes, it is thereby conceded that there is, nevertheless, only one substance of the same attribute; but if their diversity of modes, then, substance being prior in order of time to its modes, it must be considered independent of them – that is (per def. three and six,) cannot be conceived as distinguished from another – that is (per prop, four,) there cannot be many substances, but only one substance. – Q. E. D.
VI. One substance cannot be created by another substance. Dem. There cannot be two substances with the same attributes (per prop, five) – that is (per prop. two,) that hare anything in common with each other; and, therefore (per prop, three,) one cannot be the cause of the other.
Corollary 1. Hence it follows that substance cannot be created by anything else. For there is nothing in nature except substance and its modes (per axiom one, and def. three and five.) Now, this substance, not being produced by another, is self-caused.
Corollary 2. This proposition is more easily to be demonstrated by the absurdity of its contradiction; for if substance can be produced by anything else, the conception of it would depend on the conception of the cause (per axiom four,) and hence (per def. three,) it would not be substance.
VII. It pertains to the nature of substance to exist. Dem. Substance cannot be produced by anything else (per coroli. prop, six,) and is therefore the cause of itself – that is (per def. one,) its essence necessarily involves existence; or it pertains to the nature of substance to exist. – Q. E. D.
VIII. All substance is necessarily infinite. Dem. There exists but one substance of the same attribute; and it must either exist as infinite or finite. But not finite, for (per def. two) as finite it must be limited by another substance of the same nature, and in that case there would be two substances of the same attributes, which (per prop, five) is absurd. Substance therefore is infinite. – Q. E. D.
"Scholium I. – I do not doubt but that to all who judge confusedly of things, and are not wont to inquire into first causes, it will be difficult to admit the demonstration of prop. 7, because they do not sufficiently distinguish between the modifications of substances, and substances themselves, and are ignorant of the manner in which things are produced. Hence it follows, that the commencement which they see natural things have, they attribute to substances; for he who knows not the true cause of things, confounds all things, and feigns that trees talk like men; that men are formed from stones as well as from seeds, and that all forms can be changed into all other forms. So, also, those who confound the divine nature with the human, naturally attribute human affections to God, especially as they are ignorant of how these affections are produced in the mind. If men attended to the nature of substance, they would not, in the least, doubt proposition seven; nay, this proposition would be an axiom to all, and would be numbered among common notions. For by substance they would understand that which exists in itself, and is concerned through itself —i. e., the knowledge of which does not require the knowledge